Semiconductor device and temperature characteristic test method thereof
12535367 ยท 2026-01-27
Assignee
Inventors
- Tadashi Kameyama (Tokyo, JP)
- Fumiki KAWAKAMI (Tokyo, JP)
- Tetsuhiro Koyama (Tokyo, JP)
- Masataka Minami (Tokyo, JP)
Cpc classification
H10W40/00
ELECTRICITY
G05F3/30
PHYSICS
G01K2219/00
PHYSICS
International classification
G05F3/30
PHYSICS
Abstract
Before a temperature characteristic of a band gap reference circuit is tested, temperature dependencies of a reference voltage and an absolute temperature proportional voltage for a plurality of samples are measured. When the temperature characteristic is tested, based on a difference Vref between the reference voltage of the band gap reference circuit at a predetermined temperature and a median value of the reference voltages of the plurality of samples, a difference Vptat between the absolute temperature proportional voltage of the band gap reference circuit at a predetermined temperature and a median value of the absolute temperature proportional voltages of the plurality of samples is calculated.
Claims
1. A temperature characteristic test method for a semiconductor device comprising a band gap reference circuit for outputting a reference voltage and an absolute temperature proportional voltage, the method comprising: before testing a temperature characteristic of the band gap reference circuit, measuring temperature dependencies of the reference voltage and the absolute temperature proportional voltage for a plurality of samples; and calculating a first difference between the reference voltage of the band gap reference circuit at a predetermined temperature and a median value of the reference voltages of the plurality of samples; calculating a second difference between the absolute temperature proportional voltage of the band gap reference circuit at the predetermined temperature and a median value of the absolute temperature proportional voltages of the plurality of samples; and testing the temperature characteristic based on the first difference and the second difference.
2. The temperature characteristic test method according to claim 1, when testing the temperature characteristic, a ratio of the first difference and the second difference is constant regardless of temperature.
3. The temperature characteristic test method according to claim 1, when testing the temperature characteristics, a lower limit temperature and an upper limit of operation guarantee temperature are set to the semiconductor device, and the second difference is calculated based on an average value of the first difference at the lower limit temperature and the first difference at the upper limit temperature.
4. The temperature characteristic test method according to claim 1, wherein an aging degradation is determined based on an amount of change in a difference between a plurality of reference divided voltages obtained by dividing the reference voltage outputted from the band gap reference circuit of which the temperature characteristic is measured.
5. The temperature characteristic test method according to claim 4, wherein the band gap reference circuit is a first band gap reference circuit, and outputs a first reference voltage as the reference voltage, wherein the semiconductor device further comprising a second band gap reference circuit for outputting a second reference voltage formed in a different power supply region from the first band gap reference circuit, and wherein the aging degradation is determined based on an amount of change in a difference between a plurality of reference divided voltages obtained by dividing the second reference voltage outputted from the second band gap reference circuit of which a temperature characteristic is measured.
6. The temperature characteristic test method according to claim 1, wherein the band gap reference circuit is a first band gap reference circuit, and outputs a first reference voltage as the reference voltage, when testing a temperature characteristic of a second band gap reference circuit for outputting a second reference voltage, dividing the first reference voltage outputted from the first band gap reference circuit of which the temperature characteristic is measured into a first reference divided voltage, converting the first reference divided voltage to a first digital signal by the first reference voltage as a reference in a first A/D converter, converting the first reference divided voltage to a second digital signal by the second reference voltage as a reference in a second A/D converter, and testing the temperature characteristic of the second band gap reference circuit based on a difference between the first digital signal and the second digital signal.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
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DETAILED DESCRIPTION
(17) For clarity of explanation, the following description and drawings are appropriately omitted and simplified. In addition, the elements described in the drawings as functional blocks for performing various processes can be configured as CPUs (Central Processing Unit), memories, and other circuits in terms of hardware, and are realized by programs loaded into the memories in terms of software. Accordingly, those skilled in the art will understand that these functional blocks can be realized in various forms by hardware alone, software alone, or a combination thereof, and the present invention is not limited to any of them. In the drawings, the same elements are denoted by the same reference numerals, and a repetitive description thereof is omitted as necessary.
First Embodiment
(18) (Structure of Semiconductor Device)
(19) First, referring to
(20) As shown in
(21) The reference voltage Vref1 is constant with respect to a temperature at a predetermined temperature range. Here, constant, as a matter of course, has a certain tolerance, it is not necessary to be completely constant. The reference voltage Vref1 is an analog voltage signal, and is outputted to the outside of the semiconductor device 100 via an external terminal T1.
(22) On the other hand, the absolute temperature proportional voltage Vptat1 is proportional to the absolute temperature. The absolute temperature proportional voltage Vptat1 is an analog voltage signal, and is outputted to the outside of the semiconductor device 100 via an external terminal T2.
(23) Thus, the band gap reference circuit BGR1 is a reference voltage generating circuit for generating a constant reference voltage Vref1 with respect to temperature. Furthermore, the band gap reference circuit BGR1 generates the absolute temperature proportional voltage Vptat1, and has a function as a temperature sensor capable of detecting the temperature.
(24) Here,
(25) The band gap reference circuit BGR1 shown in
(26) As shown in
(27) As shown in
(28) The output terminal of the amplifier AMP outputs the reference voltage Vref1 and is commonly connected to the bases of the bipolar transistors BT1 and BT2. The negative feedback loop of the amplifier AMP controls the collector current of the bipolar transistors BT1 and BT2 to be equal.
(29) An analog buffer circuit such as a voltage follower may be provided between the output terminal of the amplifier AMP and the external terminal T1 for outputting the reference voltage Vref1 to the outside.
(30) As shown in
(31) An analog buffer circuit such as a voltage follower may be provided between the node between the resistor R3 and the resistor R4 and the external terminal T2 for outputting the absolute temperature proportional voltage Vptat1 to the outside.
(32) In
(33) Incidentally, when the base-emitter voltage of the bipolar transistor BT1 is Vbe1, a difference Vbe of the base-emitter voltages Vbe1, Vbe2 of the bipolar transistors BT1, BT2 is expressed by Vbe=Vbe2Vbe1. As shown in
(34) The circuit shown in
(35) Here,
(36) When the collector current of the bipolar transistor BT1 and the collector current of the bipolar transistor BT2 are set to match each other, Vref1=Vbe2+Vptat1 is held, but in some cases, the collector current of the bipolar transistor BT1 and the collector current of the bipolar transistor BT2 are intentionally set to be shifted from each other due to the circuit-design. Therefore, in
(37) As shown in
(38) The predetermined temperature range is, for example, the range of guaranteed operating temperature for the semiconductor device 100 (for example, 40 to 125 C.)
(39) As described above, the band gap reference circuit BGR1 has a variation in temperature characteristics, for example, based on manufacturing variations. Therefore, when manufacturing the semiconductor device 100, the temperature characteristics of the BGR circuit in each semiconductor device is tested so that the temperature can be accurately measured in the range of the guaranteed operating temperature.
(40) In the semiconductor device 100 according to the present embodiment, before the temperature characteristic of the band gap reference circuit BGR1 is tested, the temperature dependency of the reference voltage Vref1 and the absolute temperature proportional voltage Vptat1 are measured in advance for a plurality of samples. For example, each sample is put in a constant temperature chamber, at a temperature error of 1 C. or less, and the reference voltage Vref1 and the absolute temperature proportional voltage Vptat1 at each temperature are measured. The number of samples is, for example, 100 or more. More specifically, the number of samples is about hundreds to thousands.
(41) Here,
(42) As shown in
(43)
(44) As shown in
(45) Here, each of
(46) The inventors found that the ratio Vptat1/Vref1 is substantially constant regardless of temperature, and becomes substantially the same value regardless of the sample.
(47) In this specification, the median value includes not only the median value in the exact definition but also the average value. In addition, the variations in the reference voltage Vref1 and the absolute temperature proportional voltage Vptat1 are normally distributed, so that the average value and the median value in the exact definition approximately match with each other.
(48) In the semiconductor device 100 according to the present embodiment, by utilizing the variation characteristics of such a reference voltage Vref1 and the absolute temperature proportional voltage Vptat1, the temperature characteristic of the band gap reference circuit BGR1 is tested. Specifically, the temperature characteristic of the band gap reference circuit is tested by calculating Vptat1 indicating the temperature characteristic based on Vref1 with little change in temperature.
(49) Therefore, in the semiconductor device 100 according to the present embodiment, even in an environment in which the tested temperature of the semiconductor device 100 is not accurately known, it is possible to more accurately test the temperature characteristic of the band gap reference circuit BGR1.
(50) A method for testing the temperature characteristic of the band gap reference circuit BGR1 will be described below.
(51) (Method for Testing Temperature Characteristic)
(52) Next, referring to
(53)
(54)
(55)
(56) First, in
(57) As shown in
(58) That is, since the calculated Vref1Vref1 holds, the calculated Vref1 is assumed to Vref1.
(59) Next, as shown in
(60) The calculated Vptat1 is an eigenvalue showing the temperature characteristics of the respective band gap reference circuit BGR1.
(61) As also shown in
(62) Specifically, as described later, the calculated Vptat1 is converted to a digital signal, for example, and stored in a storage unit such as a fuse bit in the controller for controlling the band gap reference circuit BGR1.
(63) Further, as shown in
(64) That is, since Vptat_m(Tm)=Tm+, the measuring temperature Tm ( C.) is obtained from Tm={Vptat_m (Tm)}/. As described above, when testing the temperature characteristic of the band gap reference circuit BGR1, Vptat1 indicating the temperature characteristic is calculated using the finding, based on the relationship that Vptat1/Vref1 is constant found by the inventors, that Vref1 has little change with temperature. Then, by using the calculated Vptat1, the absolute temperature proportional voltage Vptat1 of the band gap reference circuit BGR1 is corrected.
(65) Here, in
(66) In contrast, in the semiconductor device 100 according to the present embodiment, when testing the temperature characteristic Vptat1 showing the temperature characteristic is calculated based on Vref1 with small change with temperature shown in
(67) Subsequently, referring to
(68)
(69) However,
(70) First, as shown in
(71) As shown in
(72) That is, since the calculated Vref1Vref1 holds, the calculated Vref1 is assumed to Vref1.
(73) Next, as shown in
(74) Calculated Vptat1 is an eigenvalue showing the temperature characteristic of the band gap reference circuit BGR1.
(75) As also shown in
(76) Specifically, as described later, the calculated Vptat1 is converted to a digital signal, for example, and stored in a storage unit such as a fuse bit in the controller for controlling the band gap reference circuit BGR1.
(77) Further, as shown in
(78) As shown in
(79) As described above, when testing the temperature characteristic of the band gap reference circuit BGR1, Vptat1 indicating the temperature characteristic is calculated using the finding, based on the relationship that Vptat1/Vref1 is constant found by the inventors, that Vref1 has small change with temperature. Then, the calculated Vptat1 is used to correct the absolute temperature proportional voltage Vptat1 of the band gap reference circuit BGR1.
(80) Here, in
(81) In contrast, in the semiconductor device 100 according to the present embodiment, when testing the temperature characteristic, Vptat1 showing the temperature characteristic is calculated based on Vref1 temperature with small change as shown in
(82) Returning to
(83) On the other hand, returning back to
(84) Therefore, when calculating Vptat1, it is preferable to use an average of Vref1 obtained when the measuring temperatures Tm ( C.) are both in the vicinity of 40 C. and in the vicinity of 125 C. Thus, the calculated value of the difference Vref1 between the reference voltage Vref1 and the median value Vref_m of the reference voltages can be made closer to the actual value.
Second Embodiment
(85) (Structure of Semiconductor Device)
(86) Next, with reference to
(87) As shown in
(88) As shown in
(89) Similar to that of the semiconductor device 100 according to the first embodiment shown in
(90) As shown in
(91) As shown in
(92) The temperature sensor module THS3 is formed in a power supply area PD2. The power supply area PD2 is an area where the power supply voltage differs from the power supply voltage of the power supply area PD1. The power supply area PD2 is surrounded by a power supply isolation cell PICT, and the power supply area PD1 and the power supply are separated.
(93) The temperature sensor module THS4 is formed in a power supply area PD3. The power supply area PD3 is an area where the power supply voltage is shut off at the time of low power consumption mode (for example, sleep mode). The power supply area PD3 is surrounded by a power supply isolation cell PIC2, and the power supply area PD1 and the power supply are separated.
(94) Note that the semiconductor device 200 does not need to include both the power supply areas PD2 and PD3, and only one of the power supply areas PD2, PD3 may be included in the semiconductor device 200.
(95) Furthermore, the number of temperature sensor modules may be a plurality, and is not limited in any way.
(96) Here, the temperature characteristic of the temperature sensor module THS1 is tested by the temperature characteristic test method described in the first embodiment. As shown in
(97) As will be described in more detail below, the reference voltages Vrl1 and Vrh1 are generated from the reference voltage Vref1 in the temperature sensor module THS1 whose temperature characteristic is tested. Each of the temperature sensor modules THS2 to THS4 can test the temperature characteristics of the band gap reference circuits BGR2 to BGR4 based on the reference voltages Vrl1, Vrh1.
(98) (Detailed Circuit Configuration of Semiconductor Device)
(99) Next, with reference to
(100) First, the temperature sensor module THS1 will be described.
(101) As shown in
(102) The band gap reference circuit BGR1 is the same as the band gap reference circuit BGR1 according to the first embodiment shown in
(103) As shown in
(104) The reference voltages Vrm11, Vrm12 (Vrm12>Vrm11) are the same level of the absolute temperature proportional voltage Vptat1 at a predetermined temperature which is lower than the upper limit temperature and higher than the lower limit of the operation guarantee temperature for the semiconductor device 200.
(105) Note that the semiconductor device 200 does not require both the reference voltages Vrm11 and Vrm12. The reference voltages between the reference voltage Vrl1 and the reference voltage Vrh1 are not limited to the reference voltages Vrm11 and Vrm12, and the number of the reference voltages between the reference voltage Vrl1 and the reference voltage Vrh1 may be one or three or more.
(106) As shown in
(107) The selector SLa1 selects any one of the input voltage signals based on the selection control signal sca1 outputted from the controller CTR1.
(108) The reference voltage Vref1 is inputted to the selector SLb1. The selector SLb1 selects the reference voltage Vref1 based on the selection control signal scb1 outputted from the controller CTR1.
(109) In
(110) Any one analog voltage signal of the absolute temperature proportional voltage Vptat1 and the reference voltages Vrl1, Vrm11, Vrm12 and Vrh1 is inputted to the A/D converter ADC1 via the selector SLa1.
(111) Further, the reference voltage Vref1 which is an analog voltage signal is inputted to the A/D converter ADC1.
(112) The A/D converter ADC1 converts the voltage signal inputted via the selector SLa1 into a digital voltage signal Vd1 using the reference voltage Vref1 inputted via the selector SLb1 as a reference signal. That is, the digital voltage signal Vd1 includes A/D converted digital signal from the absolute temperature proportional voltage Vptat1 and the reference voltages Vrl1, Vrm11, Vrm12 and Vrh1.
(113) The digital voltage signal Vd1 outputted from the A/D converter ADC1 is stored in a fuse bit FB1 of the controller CTR1.
(114) The controller CTR1 controls the temperature sensor module THS1. Specifically, as shown in
(115) Further, as shown in
(116) The controller CTR1 may be disposed outside the temperature sensor module THS1. Further, the fuse bit FB1 may be disposed outside the controller CTR1.
(117) Here, the temperature characteristic of the temperature sensor module THS1 is tested by the temperature characteristic test method described in the first embodiment.
(118) As shown in
(119) Next, the temperature sensor module THS2 will be described.
(120) The temperature sensor module THS2 has the same circuit configuration as that of the temperature sensor module THS1. Specifically, the temperature sensor module THS2 has the band gap reference circuit BGR2, selectors SLa2 and SLb2, an A/D converter ADC2, and the controller CTR2.
(121) Incidentally, the temperature sensor modules THS3 and THS4 have the same circuit configuration and operation as the temperature sensor module THS2, so the description thereof will be omitted.
(122) Like the band gap reference circuit BGR1 according to the first embodiment shown in
(123) On the other hand, as shown in
(124) As shown in
(125) As shown in
(126) The selector SLa2 selects any one of the input voltage signals based on the selection control signal sca2 outputted from the controller CTR2.
(127) Like the selector SLb1, the reference voltage Vref1 is inputted to the selector SLb2. Furthermore, the reference voltages Vrl1 and Vrh1 outputted from the temperature sensor module THS1 are also inputted to the selector SLb2.
(128) The selector SLb2 selects any one of the inputted voltage signals based on the selection control signal scb2 outputted from the controller CTR2.
(129) Any one analog voltage signal of the absolute temperature proportional voltage Vptat2 and the reference voltages Vref2, Vrl2, Vrm21, Vrm22 and Vrh2 is inputted to the A/D converter ADC2 via the selector SLa2.
(130) Further, any one analog voltage signal of the reference voltages Vref2, Vrl1 and Vrh1 is inputted to the A/D converter ADC2 via the selector SLb2.
(131) The A/D converter ADC2 converts the absolute temperature proportional voltage Vptat2 and the reference voltages Vrl2, Vrm21, Vrm22 and Vrh2 inputted via the selector SLa2 to the digital voltage signal Vd2 by the reference voltage Vref2 inputted via the selector SLb2 as a reference signal. That is, the digital voltage signal Vd2 includes an A/D converted digital signal from the absolute temperature proportional voltage Vptat2 and the reference voltages Vrl2, Vrm21, Vrm22 and Vrh2.
(132) On the other hand, the A/D converter ADC2 also converts the reference voltage Vrl1 and Vrh1 inputted via the selector SLb2 to the digital voltage signal Vd2 by the reference voltage Vref2 inputted via the selector SLa2 as a reference signal. That is, the digital voltage signal Vd2 also includes an A/D converted digital signal from the reference voltages Vrl1 and Vrh1.
(133) The digital voltage signal Vd2 outputted from the A/D converter ADC2 is stored in the fuse bit FB2 of the controller CTR2.
(134) The controller CTR2 controls the temperature sensor module THS2. Specifically, as shown in
(135) Here, the temperature characteristic of the temperature sensor module THS1 is tested by the temperature characteristic test method described in the first embodiment.
(136) As shown in
(137) The following describes a method of testing the temperature characteristic of the band gap reference circuit BGR2.
(138) (Method for Testing Temperature Characteristic)
(139) Next, referring to
(140) First, as shown in
(141) In the A/D convertor ADC2, the reference voltages Vrl1 and Vrh1 are converted to the digital voltage signal Vd2 by the reference voltage Vref2 inputted via the selector SLa2 as a reference signal. The digital voltage signal Vd2 is stored in the fuse bit FB2.
(142) Here, the digital voltage signals of the A/D converted reference voltages Vrl1, Vrh1 with the reference voltage Vref2 as reference signals are defined as D_ref2_rl1 and D_ref2_rh1 (not shown).
(143) In the A/D converter ADC1 of the temperature sensor module THS1, the reference voltages Vrl1 and Vrh1 are converted to the digital voltage signals Vd1 by the reference voltage Vref1 inputted via the selector SLb1 as a reference signal. The digital voltage signals Vd1 are stored in the fuse bit FB1.
(144) Here, the digital voltage signals of the A/D converted reference voltages Vrl1, Vrh1 with the reference voltage Vref1 as a reference are defined as D_ref1_rl1 and D_ref1_rh1 (not shown).
(145) Here, referring back to
(146) Since the reference voltage Vrl1 is common between the digital voltage signal D_ref2_rl1 of the reference voltage Vrl1 with reference to the reference voltage Vref2 and the digital voltage signal D_ref1_rl1 of the reference voltage Vrl1 with reference to the reference voltage Vref1, the difference between the digital voltage signal D_ref2_rl1 and the digital voltage signal D_ref1_rl1 holds the following equation (1).
D_ref2_rl1D_ref1_rl1=D_ref2D_ref1(1)
(147) In Equation (1), D_ref2 is a digital value of Vref2, D_ref1 is a digital value of Vref1. That is, the right side of Equation (1) is the digital value of Vref2Vref1. Therefore, the following equation (2) holds.
Vref2Vref1D_ref2_rl1D_ref1_rl1(2)
(148) Since Vref1 is known, by deforming equation (2), Vref2 can be obtained.
Vref2D_ref2_rl1D_ref1_rl1+Vref1
(149) Here, the difference between the absolute temperature proportional voltage Vptat2 outputted from the band gap reference circuit BGR2 and the median value Vptat_m of the absolute temperature proportional voltages is defined as Vptat2. As described in the first embodiment, Vptat2 can be obtained, as an eigenvalue showing the temperature characteristic of the band gap reference circuit BGR2, based on the relationship that Vptat2/Vref2 is constant.
(150) Thus, by using the reference voltage Vrl1 outputted from the temperature sensor module THS1 whose temperature characteristic is tested in advance, it is possible to test the temperature characteristics of the band gap reference circuit BGR2.
(151) Similarly, since the reference voltage Vrh1 is common between the digital voltage signal D_ref2_rh1 of the reference voltage Vrh1 with reference to the reference voltage Vref2 and the digital voltage signal D_ref1_rh1 of the reference voltage Vrh1 with reference to the reference voltage Vref1, the difference between the digital voltage signal D_ref2_rh1 and the digital voltage signal D_ref1_rh1 holds the following equation (3).
D_ref2_rh1D_ref1_rh1=D_ref2D_ref1(3)
(152) As described above, the right side of Equation (3) is the digital value of Vref2Vref1.
(153) Therefore, the following equation (4) holds.
Vref2Vref1D_ref2_rh1D_ref1_rh1(4)
(154) Since Vref1 is known, by deforming equation (4), Vref2 can be obtained.
Vref2D_ref2_rl1D_ref1_rl1+Vref1
(155) Therefore, from the relationship that Vptat2/Vref2=is constant, Vptat2 can be obtained as an eigenvalue showing the temperature characteristic of the band gap reference circuit BGR2
(156) Thus, even by using the reference voltage Vrh1 outputted from the temperature sensor module THS1 whose temperature characteristic is tested in advance, it is possible to test the temperature characteristic of the band gap reference circuit BGR2.
(157) Incidentally, Vptat2 may be determined using any one of the reference voltages Vrl1 and Vrh1 outputted from the temperature sensor module THS1 whose temperature characteristic is tested in advance. However, it is preferable to determine Vptat2 by using the average value of Vref2 calculated from both the reference voltages Vrl1 and Vrh1.
(158) Here,
(159) As shown in
(160) Similarly, the absolute temperature proportional voltage Vptat2 outputted from the band gap reference circuit BGR2 whose temperature characteristic is tested in advance is inputted to the A/D converter ADC2 via the selector SLa2. In the A/D converter ADC2, the absolute temperature proportional voltage Vptat2 is converted to the digital voltage signal Vd2 by the reference voltage Vref2 inputted via the selector SLb2 as a reference signal. The digital voltage signal Vd2 is stored in the fuse bit FB2.
(161) (Method for Determining Aging Degradation)
(162) Next, referring to
(163) As shown in
(164) Similarly, in the temperature sensor module THS2, the reference voltages Vrl2, Vrm21, Vrm22 and Vrh2 obtained by dividing the reference voltage Vref2 by the ladder resistor are inputted to the A/D converter ADC2 via the selector SLa2. In the A/D convertor ADC2, the reference voltages Vrl2, Vrm21, Vrm22 and Vrh2 are converted to digital voltage signals Vd2 by the reference voltage Vref2 inputted via the selector SLb2 as a reference signal. The digital voltage signals Vd2 are stored in the fuse bit FB2.
(165) Here,
(166) In each of
(167) In
(168) As shown in
(169) In
(170) As shown in
(171) As described above, in the semiconductor device 200 according to the present embodiment, the aging degradation can be determined based on the amount of changes in the difference Vrl, Vrm and Vrh, of the reference voltages Vrl1, Vrm11, Vrm12, Vrh1.
(172) Similarly, the aging degradation can be determined for the temperature sensor modules THS2 to THS4.
(173) In Patent Document 2, it is necessary to separately provide a temperature sensor module for determining the aging degradation in the vicinity of the temperature sensor module. However, in the semiconductor device 200 according to the present embodiment, that is not needed.
(174) Also, the aging degradation rates of the temperature sensor modules THS1 and THS2 formed in the same power supply area PD1 are similar. In contrast, the aging degradation rates of the temperature sensor modules THS3 and THS4 formed in the different power supply areas PD2 and PD3, are different since the power supply voltage and voltage application time are different.
(175) In such a case, in Patent Document 2, a temperature sensor module for determining the aging degradation is required to provide for each power supply areas PD1, PD2, PD3.
(176) In contrast, in the semiconductor device 200 according to the present embodiment, the temperature sensor modules THS1 to THS4 can determine the aging degradation. Therefore, the temperature sensor modules THS3 and THS4 formed in the different power supply areas PD2 and PD3 can also determine the aging degradation appropriately.
(177) The aging degradation may be determined using any of the reference voltage differences Vrl, Vrm and Vrh. Further, for example, the aging degradation may be determined using the difference between the reference voltages Vrl1 and Vrh1.
(178) The program described above includes a group of instructions (or software code) for causing a computer to perform one or more of the functions described in the embodiment when loaded into the computer. The program may be stored on a non-temporary computer-readable medium or on a tangible storage medium. By way of illustration, but not limitation, computer-readable or tangible storage media may include RAM(Random-Access Memory), ROM(Read-Only Memory, flash memory, SSD(Solid-State Drive), or other memory technologies, CD-ROM, DVD(Digital Versatile Disc), Blu-ray disks or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage, or other magnetic storage devices. The program may be transmitted on a temporary computer readable medium or communication medium. By way of example and not limitation, a temporary computer readable medium or communication medium includes an electrically, optically, acoustically, or other type of propagating signal.
(179) Although the invention made by the inventor has been specifically described based on the embodiment, the present invention is not limited to the embodiment already described, and it is needless to say that various modifications can be made without departing from the gist thereof.